Name ______________________________________ Date ____________________________ Period _______
What Fun! It's:
Practice with Scientific Notation!
Review of Scientific Notation
Scientific notation provides a place to hold the zeroes that come after a whole number or
before a fraction. The number 100,000,000 for example, takes up a lot of room and takes time
to write out, while 108 is much more efficient.
Though we think of zero as having no value, zeroes can make a number much bigger or
smaller. Think about the difference between 10 dollars and 100 dollars. Even one zero can
make a big difference in the value of the number. In the same way, 0.1 (one-tenth) of the US
military budget is much more than 0.01 (one-hundredth) of the budget.
The small number to the right of the 10 in scientific notation is called the exponent. Note that
a negative exponent indicates that the number is a fraction (less than one).
The line below shows the equivalent values of decimal notation (the way we write numbers
usually, like "1,000 dollars") and scientific notation (103 dollars). For numbers smaller than
one, the fraction is given as well.
smaller
Fraction
1/100
Decimal notation
bigger
1/10
0.01 0.1
1
10
100
1,000
____________________________________________________________________________
Scientific notation
10-2
10-1
100
101
102
103
Practice With Scientific Notation
Write out the decimal equivalent (regular form) of the following numbers that are in scientific
notation.
Section
A:
1)
102
=
_______________
4)
10-2
=
_________________
2)
104
=
_______________
5)
10-5
=
_________________
107 =
_______________
6)
100
3)
Model:
101
=
10
=
__________________
Section B:
Model:
2 x 102
=
200
7)
3 x 102
=
_________________
10)
6 x 10-3
8)
7 x 104
=
_________________
11)
900 x 10-2
=
______________
9)
2.4 x 103
=
12)
4 x 10-6
=
_________________
Section C:
Model:
13)
10
_______________
=
________________
Now convert from decimal form into scientific notation.
1,000 = 103
=
_____________________
16)
0.1
14)
100 =
_____________________
17)
0.0001
15)
100,000,000 = _______________
18)
1
Section D:
Model:
19)
400
=
20)
60,000
21)
750,000
2,000
=
=
=
_____________________
=
_______________________
2 x 103
____________________
22)
0.005 =
=
__________________
23)
0.0034
_________________
24)
0.06457
=
__________________
____________________
=
__________________
=
_________________
More Practice With Scientific Notation
Perform the following operations in scientific notation. Refer to the introduction if you need
help.
Section E: Multiplication (the "easy" operation - remember that you just need to multiply the
main numbers and add the exponents).
Model: (2 x 102) x (6 x 103) =
12 x 105 =
1.2 x 106
Remember that your answer should be expressed in two parts, as in the model above. The first
part should be a number less than 10 (eg: 1.2) and the second part should be a power of 10 (eg:
106). If the first part is a number greater than ten, you will have to convert the first part. In the
above example, you would convert your first answer (12 x 105) to the second answer, which
has the first part less than ten (1.2 x 106). For extra practice, convert your answer to decimal
notation. In the above example, the decimal answer would be 1,200,000
scientific notation
___________________
decimal notation
25)
(1 x 103) x (3 x 101) =
26)
(3 x 104) x (2 x 103) = ___________________
____________________
27)
(5 x 10-5) x (11 x 104) = __________________
____________________
28) (2 x 10-4) x (4 x 103) = ___________________
____________________
____________________
Section F: Division (a little harder - we basically solve the problem as we did above, using
multiplication. But we need to "move" the bottom (denomenator) to the top of the fraction. We
do this by writing the negative value of the exponent. Next divide the first part of each
number. Finally, add the exponents).
Model:
(12 x 103)
----------- =
(6 x 102)
2 x (103 x 10-2) = 2 x 101 = 20
Write your answer as in the model; first convert to a multiplication problem, then solve the
problem.
multiplication problem
29)
30)
(8 x 106) / (4 x 103)
=
__________________
(3.6 x 108) / (1.2 x 104) = ________________
final answer
(in sci. not.)
_____________________
_____________________
31)
(4 x 103) / (8 x 105) =
___________________
32)
(9 x 1021) / (3 x 1019) = __________________
_____________________
_____________________
Section G: Addition The first step is to make sure the exponents are the same. We do this by
changing the main number (making it bigger or smaller) so that the exponent can change (get
bigger or smaller). Then we can add the main numbers and keep the exponents the same.
Model:
(3 x 104) + (2 x 103)
=
=
=
(3 x 104) + (0.2 x 104)
3.2 x 104
32,000
First express the problem with the exponents in the same form, then solve the problem.
same exponent
final answer
33) (4 x 103) + (3 x 102)
=
____________________
_______________________
34) (9 x 102) + (1 x 104)
=
____________________
______________________
35) (8 x 106) + (3.2 x 107) = ____________________
_______________________
36) (1.32 x 10-3)+(3.44 x 10-4)= ____________________
______________________
Section H: Subtraction Just like addition, the first step is to make the exponents the same.
Instead of adding the main numbers, they are subtracted. Try to convert so that you will not
get a negative answer.
Model:
(3 x 104) - (2 x 103)
= (30 x 103) - (2 x 103)
= 28 x 103
= 2.8 x 104
same exponent
final answer
37)
(2 x 102) - (4 x 101) =
______________________
38)
(3 x 10-6) - (5 x 10-7) = ______________________
39)
(9 x 1012) - (8.1 x 109)
40)
(2.2 x 10-4) - (3 x 102) = _____________________
___________________
______________________
= ____________________ ______________________
______________________
And Even MORE Practice with Scientific Notation
(Boy are you going to be good at this.)
Positively positives!
41) What is the number of your street address in scientific notation?
42) 1.6 x 103 is what? Combine this number with Pennsylvania Avenue and what famous
residence do you have?
Necessarily negatives!
43) What is 1.25 x 10-1? Is this the same as 125 thousandths?
44) 0.000553 is what in scientific notation?
Operations without anesthesia!
45) (2 x 103) + (3 x 102) = ?
46) (2 x 103) - (3 x 102) = ?
47) (32 x 104) x (2 x 10-3) = ?
48) (9.0 x 104) / (3.0 x 102) = ?
Food for thought........and some BIG numbers
49) The cumulative national debt is on the order of $4 trillion. The cumulative amount of
high-level waste at the Savannah River Site, Idaho Chemical Processing Plant, Hanford
Nuclear Reservation, and the West Valley Demonstration Project is about 25 billion curies. If
the entire amount of money associated with the national debt was applied to cleanup of those
curies, how many dollars per curie would be spent?
Answers:
A) 1) 100
5) 0.00001
2) 10,000
6) 1
3) 10,000,000
B) 7) 300
11) 9
8) 70,000
12) 0.000004
9) 2,400
10) 0.006
C) 13) 101
17) 10-4
14) 102
18) 100
15) 108
16) 10-1
D) 19) 4x102
20) 6X104
-3
23) 3.4x10 24) 6.457x10-2
21) 7.5X105
22) 5x10-3
E) 25a) 3x104
25b ) 30,000
27a) 5.5x100 27b) 5.5
26a) 6x107
28a) 8x10-1
26b) 60,000,000
28b) 0.8
F) 29) 2x103
31) 5x10-3
32) 3x102
G) 33) 4.3x103 34) 1.09x104
35) 4x107
36) 1.664x10-3
H) 37) 1.6x102 38) 2.5x10-6
39) 8.9919x1012 40) -2.9999978x102
I) 41) Depends 42) 1600
45) 2.3x103 46) 1.7x103
49) 160 dollars/curie
43)0.125, Yes
47) 6.4x102
30) 3x104
4) 0.01
44) 5.53x10-4
48) 3x102